Question

Four moles
and
27°
a
of an ideal
gas expand reversibly
is othermally at atc from a volume
of 0.5 dm3 to 2.0 dm3 Calculate q, w, du
for
the process. (R = 8. 314 JK 'mol)?
and di​

Answer 1

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Question



Four moles of an ideal gas at 2.5 atm and 270C are compressed isothermally to half of its volume by an external pressure of 3 atm. Calculate w, q and △U.

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Solution



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Given,

Pressure of ideal gas (P)=2.5atm

Temperature of ideal gas (T)=27℃

No. of moles (n)=4 moles

Initial volume of gas ()=V=?

Now, from ideal gas equation,

PV=nRT

2.5×V=4×0.0821×300

⇒V=39.408L

Final volume (V2)=2V=239.408=19.704L

ΔV=V2−V1=19.704−39.408=−19.704L

Pext.=3atm(Given)

Now, as we know that,

W=−Pext.ΔV

∴W=−3×(−19.704)=59.112L−atm

As thw process is isothermal,

⇒ΔU=0

Now from first law of thermodynamics, i.e.,

ΔU=q+W